The size of a silver dollar.
I would go to lowes or Home Depot.. they sell 4 x 4 patch kits that come with everything. You can cut the patch down for size, but its very self explanatory on the instructions. You may need a can of spray spackel to spray before you paint.
Philip you can buy a squeeze tube or small container of Sheetrock repair mortar. Make a small round circle a little bigger than the hole in the ceiling. Poke a small hole in it’s center and thread a piece of white twine into the center of the circle. Fold or Poke this Piece of cardboard up into the ceiling hole. The string will dangle down. Gently pull down on the twine to make it flush with the ceiling. Use what you need to fill in the hole with your mortar repair caulk. Let it dry and give it another go over on the repair if necessary. Let it dry. Should look okay! Cut off the extra string or imbed in the wet mortar. You’re done!!
Put a piece of drywall mesh tape over the hole. Use no shrink drywall patching compound over the mesh with a 6" putty knife. Let it dry, sand, prime , and paint.